When it comes to television I tend to pay more attention to who wrote the script than who directed but looking at my favorite episodes I will have to go with Joseph Pevney:
He directed two of the best episodes that take place "somewhere else" in this case depression era US in City on the Edge of Forever
& Vulcan in Amok Time
. I actually felt I was being transported somewhere else from the usual in these episodes.
He directed the best comedy episode in Trouble with Tribbles
I also really love Immunity Syndrome and Journey to Babel